Political Animal: Comment On The Beatles Were Pretty Good Too Linkmeister or Brahmagupta or tsu Ch ungchi? The latter s also written ZuChongzhi. Posted by Anarch on October 29, 2003 at 1050 AM PERMALINK http://www.washingtonmonthly.com/mt/mt-comments.cgi?entry_id=2520
Extractions: Due to popular demand, I have decided to put the page from my old website onto here too..... For those who don't know, I once memorized pi to 2002 decimal places (you can say I was bored). I am even listed on the 1000-Club on Olle the Great's web site. I have now forgotten all but around the first 100 decimal places or so. A Treatise on Pi The number has always been my favourite number because of its unparalleled aesthetic beauty. On this page, I shall provide an overview of this extraordinary number: its history, properties, and its interesting facts. History of Pi Ancient History is perhaps the most famous ratio in mathematics. It is defined as the ratio between the circumference of a circle and its diameter. Throughout the ages, mathematicians have strived to find the value of . One of the earliest reference to was recorded in the Rhind Papyrus during the Egyptian Middle Kingdom, and was written by a scribe named Ahmes around 1650 BC. Ahmes began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things", and made passing remarks that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which comprises of various mathematical problems and their solutions, the area of a circle is found using a rough sort of It is interesting to note that the number is also indrectly quoted in the Bible. There is a little-known verse that reads
Home Page Of MA 2108 And MA2108S we obtain that Pi is about 3.14159264, a little more accurate than what our1500 years old ancestor did. tsu Ch ung chi ×æ³åÖ®(430501) http://www.math.nus.edu.sg/~matwujie/Fall05/
Extractions: MA 2108, Fall 2005 Problem-based learning of this module Announcement Important Notes on MA2108 and MA3110 Text Books: R. G. Bartle and D. R. Sherbert, Introduction to real analysis , 3rd edition, John Wiley, 2000. ( Compulsory reading Relevant Sections and Suggested Exercises from Bartle and Sherbert's book W. Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill, 1976. ( Supplementary reading Manfred Stoll, Introduction to real analysis , 2nd Edition, Addison Wesley Longman, Inc. press, 2001. James Stewart, Calculus , 4th Edition, Brooks/Cole Publishing Company press, 1999. Lecture Notes, consisting of 235 pages. Packed lecture notes 85 pages Syllabus Completeness axiom of the real number system. Sequences, limits (epsilon-N definition), monotone convergence theorem, Cauchy's criterion for convergence, sup, inf, lim sup and lim inf of a sequence. Infinite series, Cauchy's criteria, absolute and conditional convergence. Tests for convergence. Power series and the radius of convergence. Review of the elementary functions and their properties via power series. Pointwise and uniform convergence of a sequence of functions, Weierstrass M-test. Integration and differentiation of a series of functions.
Music By Numbers (His name is tsu Ch ungchi in Wade-Giles romanisation, read So Chuushi in Japanese.)Lived AD 430 to 501, and obtained the approximations 22/7 and 355/133 http://www.imaginatorium.org/books/mathmus.htm
Extractions: Thomas Levenson - "Measure for Measure" I was partly spurred into thinking about this by some nonsense I found about crop circles and "diatonic ratios". Claims that "no-one had ever previously linked mathematics to music" and stuff like that. Jamie James' book is the best to read as an antidote. Osserman is a close second, and Levenson a near miss. "Only gather 2, 3, 4, and 5 together, and the mumbo-jumbo artists of the world will construct a theory, a conspiracy, or a piece of magick." Making scales - Honest, yet ill-fitting work on the numbers Crop circles - "Diatonic ratios" perhaps, but fairly obviously bogus "Euler and Bach lived in the eighteenth century and, as was traditional at the time, they worked under the patronage of the nobility or royalty." "Beethoven and Gauss, by contrast, personified the romantic ideals of the early nineteenth century."
Sci-Philately - A History Of Science On Stamps tsu Ch ung chi (430501) was a chinese mathematician and astronomer. His approximationof pi was 355/113, which is correct to six decimal places. http://ublib.buffalo.edu/libraries/asl/exhibits/stamps/math1.html
Extractions: The beginning of mathematics was primitive man's discovery of counting; adding one and one to make two is pictured on this stamp. Upon seeing two birds, an Egyptian makes the cerebral leap to count them on his fingers. ( Detail ) This stamp is the first in a set of ten issued by Nicaragua in 1970 which features important mathematical formulas that changed the face of the earth. Besides showing the law, equation, or formula, the name of its originator, and an application, the reverse of each stamp is printed with a brief paragraph in Spanish explaining the significance of the formula and its far-reaching applications in modern life. Presumably the user can ponder this educational message while licking the stamp; whether the recipient would appreciate it or be aware of it is another matter. The illustrations contain a wealth of interesting detail, and the sci-philatelic sleuth can enjoy identifying the many clues and their relationship to the original formula. A well-known theorem in geometry is named after Pythagoras, who flourished in the 6th century BC, and was a teacher in Samos, Babylon, and Egypt: the sum of the squares of the sides of a right triangle equals the square of the hypotenuse. Actually, the so-called Pythagorean triples were known already in Babylonian times. The striking design of the Greek stamp is a visual representation of the theorem. (
The Contest Center - Pi 6, 355/113, pi + .00000 0266, tsu Ch ung chi 450AD. 7, v527 v354 - 1,pi - .00000 0190, Rubin. 7, v73 - v29 + 8/43, pi + .00000 00839, Rubin http://www.contestcen.com/pi.htm
Extractions: This is an open-ended competition to find the best possible approximations to pi (about 3.14159 26535 89793 23846 26433). A good approximation would be an expression which matches pi to more significant digits than the number of digits contained in that expression. For example, the most common approximation to pi is 22/7 which is about 3.14286. This contains 3 digits, and matches the first 3 digits of pi, so it is a fair approximation. We will consider 4 types of approximations. The first type uses only the mathematical operations of addition, subtraction, multiplication, division, and square root. It may not use other operations such as decimal fractions, exponentiation, logarithms, or any trig functions. For example, 355/113 (approximately pi+0.00000 0266) would be a valid expression, but 2 arcsin(1) would not. These approximations can be constructed with ruler and compass.
Database: Chinese Zen Masters (IRIZ) tsu-hsien, , Hoan Sosen. Puji, P u-chi, , Fujaku Songyuan Chongyue, Sung-yüan Ch ung-yüeh, , Shôgen Sûgaku http://iriz.hanazono.ac.jp/data/master00.en.html
Yet Another Story Of Pi About 150 AD, Ptolemy of Alexandria (Egypt) gave its value as 377/120 and inabout 500 AD the chinese tsu Ch ungchi gave the value as 355/113. http://www.geocities.com/CapeCanaveral/Lab/3550/pi.htm
Extractions: Undoubtedly, pi is one of the most famous and most remarkable numbers you have ever met. The number, which is the ratio of circumference of a circle to its diameter, has a long story about its value. Even nowadays supercomputers are used to try and find its decimal expansion to as many places as possible. For pi is one of those numbers that cannot be evaluated exactly as a decimal - it is in that class of numbers called irrationals. The hunt for pi began in Egypt and in Babylon about two thousand years before Christ. The Egyptians obtained the value (4/3)^4 and the Babylonians the value 3 1/8 for pi. About the same time, the Indians used the square root of 10 for pi. These approximations to pi had an error only as from the second decimal place. (4/3)^4 = 3,160493827... 3 1/8 = 3.125 root 10 = 3,16227766... pi = 3,1415926535... The next indication of the value of pi occurs in the Bible. It is found in 1 Kings chapter 7 verse 23, where using the Authorised Version, it is written "... and he made a molten sea, ten cubits from one brim to the other : it was round about ... and a line of thirty cubits did compass it round about." Thus their value of pi was approximately 3. Even though this is not as accurate as values obtained by the Egyptians, Babylonians and Indians, it was good enough for measurements needed at that time. Jewish rabbinical tradition asserts that there is a much more accurate approximation for pi hidden in the original Hebrew text of the said verse and 2 Chronicles 4:2. In English, the word 'round' is used in both verses. But in the original Hebrew, the words meaning 'round' are different. Now, in Hebrew, etters of the alphabet represent numbers. Thus the two words represent two numbers. And - wait for this - the ratio of the two numbers represents a very accurate continued fraction representation of pi! Question is, is that a coincidence or ...
The Pie Cafe: History Of Making Pi 380, Siddhanta, 3.1416. 480? tsu Ch ung chi, 3.1415926. 499, Aryabhata, 3.14156.640? Brahmagupta, 3.162277 (sq rt of 10). 800, AlKhowarizmi, 3.1416. http://library.thinkquest.org/26728/s1p2.htm
Extractions: So, Jesus Christ is born. It is a start of a new era. But hey, most of the people you see below are Eastern. Hmm... Alright. It is the people in the East who start to breakthrough Mathematics. Before Christ Long Long Ago Born of the Geeks Breakthroughs ... Technology 139 A.D. Hon Han Shu 3.1622 (sq rt of 10?) Ptolemy Chung Hing 3.16227 (sq rt of 10) Wang Fau Liu Hui Siddhanta Tsu Ch'ung Chi Aryabhata Brahmagupta 3.162277 (sq rt of 10) Al-Khowarizmi
Pi As A Series Of Images: The Imachinations Syracuso (Sicilia) Archimedes 250? bd Pi=3.1418. Alexandria new library Ptolemaios 150 ad Pi=3.14166. Hopeh/china tsu Ch ung chi 480? Pi=3.1415926 http://www.imachination.net/next100/brainstorm/pi.html
Extractions: Ist Pi völlig "normal"? telepolis , heise.de 05.08.2002 A Trillion Pieces of Pi , Science News Online, Dec. 2002 Random Generator and Normal Numbers , by Bailey und Crandall (Pdf, 2003) Pi in the sky - extracting a (surprisingly accurate) value for "pi" from the appearance of the night sky by Robert A. J. Matthews further Pi Pages on the Internet back
Disciples Of Confucius: Information From Answers.com After the death of Confucius, chi K ang asked Yen how that event had made nosensation The name is given by others as T ang (? and ?) and tsu (?), http://www.answers.com/topic/disciples-of-confucius
Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping Disciples of Confucius Wikipedia Disciples of Confucius Sima Qian makes Confucius say: The disciples who received my instructions, and could themselves comprehend them, were seventy-seven individuals. They were all scholars of extraordinary ability. The common saying is, that the disciples of the sage were three thousand, while among them there were seventy-two worthies. Here is a list of all those whose names have come down to us, as being his followers. Of the greater number it will be seen that we know nothing more than their names and surnames but some of them are mentionned in the Analects of Confucius State of Lu , the favourite of his master, whose junior he was by thirty years, and whose disciple he became when he was quite a youth. After I got Hui, Confucius remarked, the disciples came closer to me. We are told that once, when he found himself on the Nang hill with Hui, Zilu, and Zigong, Confucius asked them to tell him their different aims, and he would choose between them. Zilu began, and when he had done, the master said, It marks your bravery.
Lunar Republic : Craters tsu Ch ung chi. 17.3N. 145.1E. 28. ~ (430501), chinese mathematician andmathematician; He gave the rational approximation 355/113 to which is correct to http://www.lunarrepublic.com/gazetteer/crater_t.shtml
Extractions: Craters (T) Craters A B C D ... Return To Gazetteer Index Common Name Lat Long Diam Origin T. Mayer Johann Tobias ~ (1723-1762), German astronomer, cartographer and mathematician; first to determine the libration of the Moon. Tacchini Pietro ~ (1838-1905), Italian astronomer; director of the observatories at Modena, Palermo and the Collegio Romano. Tacitus Cornelius ~ (c. 55-120?), Roman politician, philosopher and historian. Tacquet André ~, S.J. (1612-1660), Belgian Jesuit and mathematician; his work helped pave that way for the discovery of the calculus. Taizo Japanese male name.
The Wonders Of Pi - The Pi Timeline tsu Ch ung chi, 480? 7, 3.1415926. Aryabhata, 499, 4, 3.14156. Brahmagupta, 640?1, 3.162277. AlKhowarizmi, 800, 4, 3.1416. Fibonacci, 1220, 3, 3.141818 http://people.bath.ac.uk/ma3mju/time.html
Extractions: The PI Timeline [The Pi Timeline] [The Ancients] [The Age Of Newton] [Twentieth Century] This table below is a timeline of PI since 2000 BC to almost present, it shows the approximate number used and the number of digits calculated. Era/Mathematician Date Correct Digits Calculated Approximation Found
The Imperial Dynasties Of China Yungchi. T ai-wu. Chung-ting. Wai-jen. Tsien-chia. tsu-yi. tsu-hsin. Ch iang-chia 145 - 146, Ch ung Ti. 146 - 147, chih Ti. 147 - 168, Huan Ti http://www.kessler-web.co.uk/History/KingListsFarEast/ChinaDynasties.htm
Extractions: 1766 - 1122 BC (1523 - 1028 BC) BC Ch'eng-tang T'ai-chia Wu-ling T'ai-keng Hsiao-chia Yung-chi T'ai-wu Chung-ting Wai-jen Tsien-chia Tsu-yi Tsu-hsin Ch'iang-chia Tsu-ting Nan-keng Hu-chia P'an-keng Hsiao-hsin Hsiao-yi Wu-ting Tsu-kêng Tsu-chia Lin-hsin K'ang-tin Wu-yi Wên-wu-ting Ti-yi - 1122 BC Ti-hsin CHOU / ZHOU DYNASTY 1122 - 722 BC 1122 - 722 BC Capital: Hao. Capital: Luoyang. 1100 BC Wu Wang Western Zhou. Chêng Wang K'ang Wang ar.950 BC Chao Wang Western Zhou. Mu Wang Kung Wang I Wang Hsiao Wang I Wang 878 BC Li Wang 841 BC First solid date in Chinese chronology. 827 BC Hsüan Wang 781 - 771 BC Yu Wang Western Zhou.
Continued Fractions From Euclid Till Present The continued fraction convergent p»355/113 was known to tsu Ch ung chi born inFanyang, china in 430 AD. More recently, the Swiss mathematician Lambert http://algo.inria.fr/seminars/sem98-99/vardi1-2.html
Extractions: Continued fractions have fascinated mankind for centuries if not millennia. The timeless construction of a rectangle obeying the ``divine proportion'' (the term is in fact from the Renaissance) and the ``self-similarity'' properties that go along with it are nothing but geometric counterparts of the continued fraction expansion of the golden ratio, f
Extractions: Ch'en Yin-k'o and Fu Ssu-nien Since many of the personal letters, manuscripts etc. of Fu Ssu-nien and probably of Ch'en Yin-k'o too have not yet been published or made accessible to the public this "Complete Bibliography" is far from complete. It includes all writings that have been published (most of it in collections ) or have been mentioned in research on Ch'en and Fu. If anything that already has been published is missing or if you discover any mistakes please contact me at a.schneider@let.leidenuniv.nl CMKTKCP Chin-ming-kuan ts'ung-kao ch'u-pien, by Ch'en Yin-k'o CMKTKEP Chin-ming-kuan ts'ung-kao erh-pien, by Ch'en Yin-k'o CYK Ch'en Yin-k'o CYKWC Ch'en Yin-k'o hsien-sheng wen-chi CYKLW Ch'en Yin-k'o hsien-sheng lun-wen-chi CYKLWPP Ch'en Yin-k'o hsien-sheng lun-wen-chi pu-pien FSN Fu Ssu-nien FSNCC FSNP Fu Ssu-nien Papers HLTC Han-liu-t'ang chi, by Ch'en Yin-k'o HLTC ST Han-liu-t'ang chi shih-ts'un, by Ch'en Yin-k'o HSWT Hu Shih wen-ts'un KSP Ku-shih-pien WKTCC YPSCC Yin-pin-shih chuan-chi, by Liang Ch'i-ch'ao
Extractions: Orange Coast College , Costa Mesa, California Om Mani Padme Hum! Overview: To present correlations between the Pineal Gland, the psychopharmacological molecule LSD and, its antagonistic neurotransmitter Serotonin. Brief Description of the Discovery - Historical Findings Descartes Ancient anatomy - to 14th Century Initial misinterpretations of evidence Description of the General Location of the Pineal Gland Brain sections surrounding the pineal Where the Serotonin is manufactured The location of the pineal in various animals Pacific Treefrog - Hyla regilla Sea Lamprey - Petromyzon marinus Western Fence Lizard - Sceloporus occidentalis South American mammal-like reptile - Lystrosaurus murrayi The Optic "Third Eye" Compared to the Endocrinal Pineal Gland The various animals with protruding pineal receptors Other evidence of the optical quality of the Pineal Gland Speculation of the connectional relation of the semi-mythical 'Third Eye' and the factual pineal gland Recent Findings of Pineal Function and Its Physiology Biorhythmic cycles Sex hormones and their relation to light Day/night cycles (circadian - light/dark phases) Serotonin and melatonin - their role in the Pineal Serotonin, LSD and the Pineal Gland
Prime Curios!: 113 tsu Ch ungchi (430-501 AD) and his son stated that pi is approximately 355/113.The smallest prime factor of 12345678910111213 (the concatenation of the http://primes.utm.edu/curios/page.php?number_id=109
Extractions: Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909)
From Vincent R. Johns Vjohns@cliff.backbone.uoknor.edu result was that of Lazzerini (1901), who made 34080 tosses and got pi =355/113 = 3.1415929 which, incidentally, is the value found by tsu Ch ung chi. http://www.math.niu.edu/~rusin/known-math/96/buffon
